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Interest Rates and Bond Valuation

Chapter 7

Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

Chapter Outline

• Bond Definitions

• Bond Valuation

• Interest Rate Risk

• Bond Features

• Types of Bonds

• Bond Markets & Reporting in the Press

• Interest Rates & Inflation

• Term Structure of Interest Rates 2

Bond Definitions• Bond (=IOU)

• Par value (face value)

• Coupon rate

• Coupon payment

• Maturity

• Yield to maturity

• Bond Price

• Current Yield 3

Bond Valuation

• Bond Price = PV of coupons + PV of face• Bond Price = PV annuity + PV of simple CF

• On the financial calculator use TVM keys: face value (F) = FVcoupon payment (C) = PMT, time to maturity (t) = N, yield to maturity (r) = I/Yprice = PV (the PV has the opposite sign of FV & PMT)

t

t

r)(1

F

rr)(1

1-1

C Price Bond

4

Bond Valuation Example 1

A bond has a $1,000 face value and makes annual coupon payments. If the coupon rate is 10% per year, the time to maturity is 5 years and the yield to maturity is 11% (EAR), what is the price of the bond?

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Bond Valuation Example 2

A bond has a $1,000 face value and makes semi-annual coupon payments. The coupon rate is 8% per year (APR), the time to maturity is 10 years and the annual yield to maturity is 10%, compounded semi-annually. Calculate the price of the bond.

6

Bond Valuation Example 3

Assume a bond makes annual payments and has as a $1,000 face value. The coupon rate is 8% per year, the time to maturity is 10 years, and the bond sells currently for $945. What is the implied yield to maturity?

7

Bond Valuation Example 4

What is the price of a 10-year, zero coupon bond that pays $1,000 at maturity if the YTM is 9% (assume annual compounding).

8

Interest Rate Risk

Definition: Change in price due to changes in interest rates.

- As interest rates increase, bond prices , and vice versa.

- Premium Bond:- Discount Bond:- Time to maturity is related to

interest rate risk.- The coupon rate is related to

interest rate risk .

Bond Features• 3 Main differences between debt and

equity:1.

2.

3.

• Indenture: Contract between the company and the bondholders– basic terms of the bonds– amount issued– collateral– seniority– repayment provisions– call provisions– protective covenants

Types of Bonds• Government Bonds • Zero Coupon Bonds

• Floating Rate Bonds

• Income Bonds

• Convertible Bonds

• Put Bonds

• TIPS (Treasury Inflation Protected Securities)11

Bond Markets & Reporting in the Press

• Primarily OTC • Large, non-transparent market• Bond quotes are available online (

www.bondsonline.com, www.finra.org)• Corporate Bond Quote example (as of 3/2006):

Current ESTName Coupon Maturity Price Yield YTM Spread UST Vol.AT&T (T) 6.25 Mar 15, 2011 102.613 6.09 5.64 68 5 51,936

• Treasury Bond Quote example (5/2006):Coupon Maturity Bid Asked Change Asked Yield8.00 Nov 21 128:07 128:08 5 5.30

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Interest Rates & Inflation

• The Fisher Effect defines the relationship between real rates, nominal rates and inflation

• (1 + R) = (1 + r)(1 + h), whereR = nominal rater = real rate h = expected inflation rate

• ApproximationR ≈ r + h

13

Interest Rates & Inflation: Example

• Investors require a real return of 15%. Assume an inflation rate of 4%. What is the nominal rate?

14

Term Structure of Interest Rates

• Term structure is the relationship between time to maturity and yields, all else equal

• Yield curve – graphical representation of the term structure

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Upward-Sloping Yield Curve

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Term Structure

Source: WSJ, 2/14/2012